Problem: Solve for $x$ : $5\sqrt{x} - 8 = 8\sqrt{x} + 7$
Solution: Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} - 8) - 5\sqrt{x} = (8\sqrt{x} + 7) - 5\sqrt{x}$ $-8 = 3\sqrt{x} + 7$ Subtract $7$ from both sides: $-8 - 7 = (3\sqrt{x} + 7) - 7$ $-15 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-15}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-5 = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.